It is well known that using a diversity scheme can improve the signal-to-noise ratio of a received information signal in a telecommunications system. A diversity scheme involves, for example, using information derived from several signals transmitted over independent fading paths to produce a single received information signal. In telecommunications systems having multiple transmit antennas (transmit diversity), a coding scheme can be used to encode the transmitted information and thereby improve reliability. Using a coding scheme with such telecommunications systems reduces errors in the received information signal.
The use of codes for improving the reliability of a telecommunications systems having multiple transmit antennas has been discussed in articles. For example, a code for providing full diversity for telecommunications system using two transmit antennas is discussed in an article by Alamouti. See S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” in IEEE Journal on Selected Areas of Communications, Vol. 16, pp. 1451-1458, November 1998, which is incorporated herein by reference in its entirety. The code of Alamouti is generalized to any number of antennas in an article by Tarokh et al. See V. Tarokh et al., “Space-time block codes from orthogonal designs,” in IEEE Trans. Inform. Theory, Vol. 45, pp. 1456-1467, July 1999, which is incorporated herein by reference in its entirety. As suggested by the title, the code of Tarokh et al. is referred to as a space-time block code.
In their article, Tarokh et al. have generalized the theory of orthogonal designs to show when a full diversity scheme is possible and how to achieve it. See id. Although the space-time block code of Tarokh et al. provides full diversity, its main goal is not to provide enhanced coding gains. See id., and V. Tarokh et al., “Space-time block codes for wireless communications: performance results,” in IEEE Journal on Selected Areas of Communications, Vol. 17, pp. 451-460, March 1999, which is incorporated herein by reference in its entirety. To achieve enhanced coding gains, one needs to concatenate another code to the space-time block code of Tarokh et al.
Space-time trellis codes combine a trellis code with an inner space-time block code to provide enhanced coding gain. Space-time trellis codes are discussed in an article by Alamouti et al. See S. Alamouti et al., “Trellis-coded modulation and transmit diversity: design criteria and performance evaluation,” in IEEE International Conference on Universal Personal Communications (ICUPC-98), Vol. 2, pp. 917-920, 1998, which is incorporated herein by reference in its entirety. The space-time trellis coding scheme of S. Alamouti et al. is used for Rayleigh fading channels with large space-time correlations in an article by Siwamogsatham et al. See S. Siwamogsatham et al., “Robust space-time coding for correlated Rayleigh fading channels,” Allerton Conference, October 2000, which is incorporated herein by reference in its entirety.
As will be understood by a person skilled in the relevant telecommunications art, the coding scheme of Alamouti et al. and Siwamogsatham et al. does not produce the maximum possible coding gain, nor does it provide a method for designing new codes for systems other than those discussed. For example, it is not clear how to design codes for telecommunications systems having different number of states or different rates than the ones discussed by Alamouti et al. and Siwamogsatham et al. Thus, there is a need for new codes having improved coding gains and a method for designing such codes.